Project description

This project aims at applying operadic techniques to motivic homotopy theory. We want to study realizations and actions of various operads in motivic spaces coming from operads in the category of schemes, like Deligne-Mumford compactifications of moduli spaces of curves and higher analogues of those. We expect a close relationship of certain such realizations due to Kato and Nakayama to little discs operads (relevant for loop space recognition principles). As a side project we will continue computations of homotopy groups of motivic spheres using the slice spectral sequence, which will also serve as testing ground for questions regarding $\mathbb{P}^1$-stabilizations.

Related publications

A.Ananyevskiy, O.Röndigs, P.A. Østvær. On very effective hermitian \(K\)-theory. Math. Z., 294(3-4):1021--1034, 2019.

O. Röndigs, M. Spitzweck und P.A. Østvær. The motivic Hopf map solves the homotopy limit problem for \(K\)-theory. Doc. Math. 23 (2018), 1405-1424.

O. Röndigs,On the \(\eta\)-inverted sphere. In ``\(K\)-Theory, volume 19 of Tata Inst. Fundam. Res. Stud. Math.'', 41--63. Tata Inst. Fund. Res., Mumbai, 2018.

O. Röndigs, M. Spitzweck, P.A. Østvær. Cellularity of hermitian K-theory and Witt-theory. In ``\(K\)-Theory, volume 19 of Tata Inst. Fundam. Res. Stud. Math.'', 35--40. Tata Inst. Fund. Res., Mumbai, 2018.

Kyle Ormsby, Oliver Röndigs, Paul Arne Østvær, Vanishing in stable motivic homotopy sheaves Forum Math. Sigma 6 (2018), Paper No. e3, 20 pp.

G. Biedermann, G. Raptis, M. Stelzer, The realization space of an unstable coalgebra, Astérisque No. 393 (2017), viii+148 pp.

Preprints

H. Heine, M. Spitzweck, A. Lopez-Avila. Infinity categories with duality and hermitian multiplicative infinite loop space machines. Preprint 2016, arXiv:1610.10043

M. Frankland, M. Spitzweck. Towards the dual motivic Steenrod algebra in positive characteristic. Preprint 2017, arXiv:1711.05230

M. Spitzweck. A Grothendieck-Witt space for stable infinity categories with duality. Preprint 2016 arXiv:1610.10044

M. Stelzer, Simplicial coalgebras over a Prüfer domain and homotopy theory. Preprint